Student Activities

Parent Activities

Teacher Activities

Worksheet: Hole Geometries in Crystals

In this worksheet, we will practice determining stoichiometries of atoms and ions in cubic lattices based on Bravais lattice type and hole occupancies.

Q1:

How many octahedral holes would you expect to find in a closed-packed crystal containing 8 atoms?

Q2:

In a face-centred cubic ionic lattice, cations of element M occupy one-eighth of the tetrahedral holes and
half of the
octahedral holes between anions of element L. What is the formula of this material?

AML23

BML43

CML32

DML34

EML3

Q3:

Which type of hole do lithium ions occupy in the cubic lattice of LiSe2?

ACubic

BOctahedral

CBoth octahedral and tetrahedral

DTetrahedral

EBoth cubic and tetrahedral

Q4:

In a hexagonal close-packed ionic lattice, cations of element M occupy two-thirds of the octahedral holes between anions of element L. What is the formula of this material?

AML2

BML2

CML

DML23

EML32

Q5:

In a cubic ionic lattice, a cation of element M is located at each corner of the unit cell and an anion of element L is located at the centre of each edge. What is the formula of this material?

AML43

BML2

CML23

DML3

EML2

Q6:

In a face-centred cubic ionic lattice, cations of element A occupy one-eighth of the tetrahedral holes between anions of element L, while cations of element Z occupy half of the octahedral holes. What is the formula of this material?

AAZL43

BAZL24

CAZL423

DAZL24

EAZL43

Q7:

The radius of a cation in a cubic ionic lattice is 70% smaller than the radius of the anion. The charges of the cation and anion are equal in magnitude. Which type of hole is the cation likely to occupy?

AOctahedral

BCubic

CBoth octahedral and tetrahedral

DTetrahedral

EBoth octahedral and cubic

Q8:

How many tetrahedral holes would you expect to find in a close-packed crystal containing 6 atoms?

Q9:

In an ionic lattice, cations of element M occupy all of the cubic holes in the simple cubic lattice formed by anions of element L. What is the formula of this material?

AML2

BML2

CML23

DML

EML32

Q10:

In the cubic unit cell of a manganese oxide, there is a manganese ion in the centre of the cell and at each of the corners. Oxide ions are located at the centre of each edge of the unit cell. What is the formula of this compound?

AMnO

BMnO3

CMnO2

DMnO23

EMnO34

Q11:

Tetrahedral holes have a coordination number of .

Q12:

In a close-packed arrangement of spheres with a uniform radius of 1.5 Å, what is the radius of the largest sphere that can occupy an octahedral hole?

Q13:

What is the size of a tetrahedral hole in a cubic close-packed system with a radius of 1.2 Å?

Q14:

NaCl and ZnS both have face-centered cubic structures. Why do the sodium ions in NaCl have a higher coordination number than the zinc ions in ZnS?

ASodium ions occupy tetrahedral holes, as they are less similar in size to chloride ions than zinc ions are to sulfide ions.

BSodium ions occupy tetrahedral holes, as they are more similar in size to chloride ions than zinc ions are to sulfide ions.

CSodium ions occupy octahedral holes, as they are less similar in size to chloride ions than zinc ions are to sulfide ions.

DSodium ions occupy octahedral holes, as they are more similar in size to chloride ions than zinc ions are to sulfide ions.

ESodium ions occupy both tetrahedral and octahedral holes, as they are more similar in size to chloride ions than zinc ions are to sulfide ions.